The stability properties of WKB methods are dual to those of the
moment recursions
in [1]}, [2]}, in that
they propagate probability
distributions outward into attenuating tails from the regions near the
mean where probability is most concentrated. Those central regions
are the main scale factors in the recursion approach, where matching
conditions must be imposed between low and high moment orders.
It is by grounding asymptotic regions in the centers of mass of probability
distributions that WKB methods provide approximate solution methods
for boundary-value problems [3]}.
